[Nengo]: Why does the intercept change when radius is changed?

[xchoo]

@zerone

when you talk about remember that in this space, does it refer to vector space where the expected/default values are between -1 and 1 or the current space?

For that, I was referring to the current space.

@zerone

The current could have any value greater than or equal to 0… right? I guess I am wrong here… I can see in response_curve plot that the current can be negative as well, but the concept of negative current is difficult to digest; can you please explain it biophysically?

This is what I was trying describe when I said that the current space is normalized between -1 and 1. To put it in biological perspective, let’s take 2 example neurons. Both neurons have an activation threshold of -55mV, and a resting membrane potential of -70mV. So, if they receive enough current for their membrane voltages to go from -70mV to -55mV, they will emit a spike.

For neuron 1, we do not add any bias voltage, so the current needed to cause the neuron to spike is 15mV/R_{mem} (where R_{mem} is the membrane resistance). Just for the sake of making numbers concrete, let’s say R_{mem} = 1, so the current needed to cause the first neuron to spike is 15mA.

Now, for neuron 2, let’s apply an inhibitory bias voltage (biologically, this could be due to the environment the neuron is in, or could be due to another neuron [that’s not in the network] providing it constant input) of -20mV. For neuron 2 then, the current needed to cause it spike would be 35mA.

So, in our little example, we know the firing threshold for the first neuron to be 15mA, and the second neuron to be 35mA. If we want to work with these number though, it gets a little cumbersome to deal with these numbers since they are on an arbitrary scale. So, what we do is we normalize these numbers to be within some scale. This scale in Nengo is from -1 to 1. For our example, let’s set 15mA to be “0”, and 50mA to be “1”. Then, the equivalent firing threshold for the first neuron would be at 0, and the second neuron would be at 0.4.

Given this example, what would a “negative” current be? Well, it would be if the neuron was receiving a excitatory bias voltage (or bias current), that makes it easier to generate a spike.

@zerone

I thought that intercepts (a parameter in neuron non-linearity phase) are defined in vector space.

I suppose I did misspeak. To me, there is no difference between a vector and a scalar (a scalar is just a single dimensional vector). But, to be precise, the encoding phase is defined in vector space (i.e., within the unit hypersphere), and the neuron non-linearity phase is defined in scalar (current) space (i.e., from -1 to 1).